You cannot 'unwatermark' the video - it is embedded into the images/frames.
You can, however, use a program to crop out the watermark.
You could also use a program to place your watermark over theirs - but you probably won't be able to make it very transparent.
Edit: technically, you can edit every single frame with some paint/graphic program (to get rid of their watermark) - but that would be insane.
Windows Movie Maker does simple video cropping.